If you are dealing with something that moves, at least something that does not move at an appreciable fraction of the speed of light, then Newton’s Laws of Motion are bound to be relevant. You can use them to understand the behaviour and trajectory of the objects in question.
In fact, the motion of virtually everything we deal with in normal life can be understood in terms of Newton’s Laws of Motion. Without them, the motion and behaviour of a great many objects in our world could not be properly understood.
They serve as the basis for much of physics, certainly much of the branch of physics known as mechanics. And have been important in several other branches of physics.
Until they were superseded by Einstein’s Relativity, his law of gravitation were used to understand the motions and behaviour of much of the celestial objects in our universe. Without an understanding of gravity as provided by Newton or Einstein’s equations, the behaviour of most of the objects in space cannot be understood.
But, the importance of this goes far beyond providing an understanding of the motion of Earthly and celestial objects. Newton was one of the first to show that many aspects of nature can be easily understood by the application of simple physical principles.
Not only that, he showed that the behaviour of these physical objects could be calculated and predicted using simple equations.
This made an immense case for the power of science, physics in particular, for understanding the universe and predicting its behaviour.
The work of Newton showed just how much of the real world could be understood and predicted using simple equations. But, not only this, it showed the immense power of induction.
This was key to Newtons immense success. He was a master of grasping the commonalities between seemingly disparate things such as rocks on Earth and comets in space and identifying general principles which applied to both kinds of entities.
We will talk further about induction in a later episode. But for now note that a key reason for Newton’s success at explaining so much of nature with a few simple principles, is his application of induction.
Another important aspect of Newton’s laws of motion is that his theory of calculus was crucial in helping to derive them. In fact, you can, as Newton did, use simple calculus to derive various of his laws of motion from previously established ones.
This illustrates the vital role mathematics plays in physics. Mathematics is the science of quantifying relationships between things. Physics of course deals with many such relationships.
What Newton did was start with something he knew to be true, such as his Second Law of Motion, and perform mathematical operations so that a consequence of this is that F equals mass times acceleration.